The parents of Trayvon Martin, the black teenager shot to death by a Hispanic neighbourhood watch captain in Florida, told hundreds of people at a march in his memory that they won't stop until they get justice for him.

"My son did not deserve to die," the teenager's father, Tracy Martin, said after thanking the crowd.

The neighbourhood watch captain, George Zimmerman, has not been charged in the shooting. Zimmerman has said the teen attacked him and he shot him in self-defence.

On Wednesday night, demonstrators chanted "We want arrests!" during the Million Hoodie March in Union Square in Manhattan.

Trayvon's mother, Sybrina Fulton, told the crowd: "My heart is in pain, but to see the support of all of you really makes a difference."

The case has sparked anger against the police department of the Orlando suburb of 53,500 people, prompting rallies and a protest in Governor Rick Scott's office on Tuesday. The Justice Department's Civil Rights Division said it was sending its community relations service to Sanford this week to "address tension in the community".

Earlier this week, the federal agency opened a civil rights probe into the shooting, and in Florida, Seminole County state attorney Norm Wolfinger said a grand jury will meet on 10 April to consider evidence in the case.

Tracy Martin said he and his son's mother found out about the march after arriving in New York City, where they have given interviews about the case. They got in touch with the organisers to say they would attend and speak to the crowd.

The timing of the teenager's parents being in the city when the march was happening was "incredible", said one of the organisers, Daniel Maree, who heard about the case earlier this week.

"I was outraged and wanted to do something about it," Maree said.

Information surrounding Trayvon's death has been coming out in the days since the shooting, including 911 calls and an account from his family's lawyer of a conversation he had with his girlfriend in the moments before his death.

Tracy Martin said he was trying to stay strong. "I don't feel this is the time to break down, even though it's a very troubling time in my life," he said. "I've told myself, when I get justice for Trayvon, then I'll have my time to break down."